# Turning Channel Noise into an Accelerator for Over-the-Air Principal Component Analysis

arXiv: https://arxiv.org/abs/2104.10095 · HTML: https://mlsanity.com/paper/2104.10095/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 20 Apr 2021.

## Builds on (most cited first, 23 of 23)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Federated Learning in Mobile Edge Networks: A Comprehensive Survey](https://mlsanity.com/paper/1909.11875/) (2019)
- [How to Escape Saddle Points Efficiently](https://mlsanity.com/paper/1703.00887/) (2017)
- [A Joint Learning and Communications Framework for Federated Learning over Wireless Networks](https://mlsanity.com/paper/1909.07972/) (2019)
- [Escaping From Saddle Points --- Online Stochastic Gradient for Tensor Decomposition](https://mlsanity.com/paper/1503.02101/) (2015)
- [Federated Learning via Over-the-Air Computation](https://mlsanity.com/paper/1812.11750/) (2018)
- [Broadband Analog Aggregation for Low-Latency Federated Edge Learning (Extended Version)](https://mlsanity.com/paper/1812.11494/) (2018)
- [Federated Learning over Wireless Fading Channels](https://mlsanity.com/paper/1907.09769/) (2019)
- [Energy Efficient Federated Learning Over Wireless Communication Networks](https://mlsanity.com/paper/1911.02417/) (2019)
- [Scheduling Policies for Federated Learning in Wireless Networks](https://mlsanity.com/paper/1908.06287/) (2019)
- [One-Bit Over-the-Air Aggregation for Communication-Efficient Federated Edge Learning: Design and Convergence Analysis](https://mlsanity.com/paper/2001.05713/) (2020)
- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems](https://mlsanity.com/paper/2006.11144/) (2020)
- [HFEL: Joint Edge Association and Resource Allocation for Cost-Efficient Hierarchical Federated Edge Learning](https://mlsanity.com/paper/2002.11343/) (2020)
- [Privacy For Free: Wireless Federated Learning Via Uncoded Transmission With Adaptive Power Control](https://mlsanity.com/paper/2006.05459/) (2020)
- [Energy-Efficient Resource Management for Federated Edge Learning with CPU-GPU Heterogeneous Computing](https://mlsanity.com/paper/2007.07122/) (2020)
- [High-Dimensional Stochastic Gradient Quantization for Communication-Efficient Edge Learning](https://mlsanity.com/paper/1910.03865/) (2019)
- [Energy-Efficient Federated Edge Learning with Joint Communication and Computation Design](https://mlsanity.com/paper/2003.00199/) (2020)
- [Improved Distributed Principal Component Analysis](https://mlsanity.com/paper/1408.5823/) (2014)
- [Hybrid Beamforming for Massive MIMO Over-the-Air Computation](https://mlsanity.com/paper/2006.04560/) (2020)
- [Gradient Statistics Aware Power Control for Over-the-Air Federated Learning](https://mlsanity.com/paper/2003.02089/) (2020)
- [Federated Principal Component Analysis](https://mlsanity.com/paper/1907.08059/) (2019)
- [Federated Over-Air Subspace Tracking from Incomplete and Corrupted Data](https://mlsanity.com/paper/2002.12873/) (2020)

## Built on by (most cited first, 14 of 14)

- [Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applications](https://mlsanity.com/paper/2111.12444/) (2021)
- [A Survey on Over-the-Air Computation](https://mlsanity.com/paper/2210.11350/) (2022)
- [Scalable Hierarchical Over-the-Air Federated Learning](https://mlsanity.com/paper/2211.16162/) (2022)
- [Over-the-Air Federated Learning and Optimization](https://mlsanity.com/paper/2310.10089/) (2023)
- [Spectrum Breathing: Protecting Over-the-Air Federated Learning Against Interference](https://mlsanity.com/paper/2305.05933/) (2023)
- [Edge Intelligence Over the Air: Two Faces of Interference in Federated Learning](https://mlsanity.com/paper/2306.10299/) (2023)
- [Over-the-Air Federated Learning via Weighted Aggregation](https://mlsanity.com/paper/2409.07822/) (2024)
- [Adaptive Federated Learning Over the Air](https://mlsanity.com/paper/2403.06528/) (2024)
- [Robust Federated Learning Over the Air: Combating Heavy-Tailed Noise with Median Anchored Clipping](https://mlsanity.com/paper/2409.15100/) (2024)
- [Over-the-Air Federated Learning: Rethinking Edge AI Through Signal Processing](https://mlsanity.com/paper/2512.03719/) (2025)
- [Accelerating Wireless Federated Learning via Nesterov's Momentum and Distributed Principle Component Analysis](https://mlsanity.com/paper/2303.17885/) (2023)
- [Byzantine-Resilient Federated PCA and Low Rank Column-wise Sensing](https://mlsanity.com/paper/2309.14512/) (2023)
- [Generation of Uncorrelated Residual Variables for Chemical Process Fault Diagnosis via Transfer Learning-based Input-Output Decoupled Network](https://mlsanity.com/paper/2404.18528/) (2024)
- [Quantized Analog Beamforming Enabled Multi-task Federated Learning Over-the-air](https://mlsanity.com/paper/2503.17649/) (2025)

## Abstract (arXiv)

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the linear structure of a dataset, which is useful for feature extraction and data compression. In this work, we propose the deployment of distributed PCA over a multi-access channel based on the algorithm of stochastic gradient descent to learn the dominant feature space of a distributed dataset at multiple devices. Over-the-air aggregation is adopted to reduce the multi-access latency, giving the name over-the-air PCA. The novelty of this design lies in exploiting channel noise to accelerate the descent in the region around each saddle point encountered by gradient descent, thereby increasing the convergence speed of over-the-air PCA. The idea is materialized by proposing a power-control scheme which detects the type of descent region and controlling the level of channel noise accordingly. The scheme is proved to achieve a faster convergence rate than in the case without power control.